Independent regulation of tumor cell migration bymatrix stiffness and confinementAmit Pathak and Sanjay Kumar1

Department of Bioengineering, University of California, Berkeley, CA 94720-1762

Edited by Dennis E. Discher, University of Pennsylvania, Philadelphia, PA, and accepted by the Editorial Board May 4, 2012 (received for reviewNovember 2, 2011)

Tumor invasion and metastasis are strongly regulated by biophy-sical interactions between tumor cells and the extracellular matrix(ECM). While the influence of ECM stiffness on cell migration,adhesion, and contractility has been extensively studied in 2D cul-ture, extension of this concept to 3D cultures that more closely re-semble tissue has proven challenging, because perturbations thatchange matrix stiffness often concurrently change cellular confine-ment. This coupling is particularly problematic given that matrix-imposed steric barriers can regulate invasion speed independentof mechanics. Here we introduce a matrix platform based onmicro-fabrication of channels of defined wall stiffness and geometrythat allows independent variation of ECM stiffness and channelwidth. For a given ECM stiffness, cells confined to narrow channelssurprisingly migrate faster than cells in wide channels or on uncon-strained 2D surfaces, which we attribute to increased polarizationof cell-ECM traction forces. Confinement also enables cells tomigrate increasingly rapidly as ECM stiffness rises, in contrast withthe biphasic relationship observed on unconfined ECMs. Inhibitionof nonmusclemyosin II dissipates this traction polarization and ren-ders the relationship between migration speed and ECM stiffnesscomparatively insensitive to matrix confinement. We test thesehypotheses in silico by devising a multiscale mathematical modelthat relates cellular force generation to ECM stiffness and geome-try, which we show is capable of recapitulating key experimentaltrends. These studies represent a paradigm for investigatingmatrix regulation of invasion and demonstrate that matrix confine-ment alters the relationship between cell migration speed and ECMstiffness.

microchannels ∣ glioblastoma ∣ cytoskeleton ∣ mechanobiology ∣polyacrylamide

Tumor cells exploit a variety of migration strategies to invadetissue and metastasize to distant anatomical sites, which in

turn requires specific biochemical and biophysical interactionsbetween these cells and the extracellular matrix (ECM) (1–4).Cell migration through the ECM may be regarded as a cyclicprocess that includes leading-edge extension of protrusionsdriven by actin polymerization, formation of cell-ECM adhesions,and trailing-edge retraction due to actomyosin contractility.While ECM-based biophysical cues have been demonstrated toinfluence all of these steps (5), ECM stiffness has emerged as aparticular parameter of interest given the observations thattumors are frequently more rigid than normal tissue and that exo-genous tissue stiffening can facilitate tumorigenesis (6–13). Muchof the field’s understanding of matrix stiffness derives from stu-dies in 2D culture, where polyacrylamide (PA) hydrogels conju-gated with full-length ECM proteins have proven a versatile androbust paradigm for the independent control of ECM stiffnessand biochemical ligand density (7–10, 13–15). For example, ECMstiffness strongly affects the migration and proliferation rate ofglioma cells (8), the expression of prognostic markers in neuro-blastoma (7), and the self-renewal and differentiation of stemcells (9, 16). Extension of these studies to 3D microenvironmentscharacteristic of most tissues has proven extremely challenginggiven that manipulations normally used to vary ECM stiffness

(e.g., variation of matrix and crosslink density) often concurrentlyalter matrix pore size, which can independently and significantlyaffect cell migration (4, 6). For example, reduction of matrix poresize has been shown to induce transitions between amoeboid andmesenchymal cell motility (3, 17, 18), and below a critical limitcan slow or arrest cell invasion due to steric hindrance (6, 19).This convolution of parameters has motivated an interest in thedevelopment of 3D ECM scaffolds that permit independent var-iation of ECM stiffness and pore size, which could significantlyimprove the field’s understanding of the biophysical regulationof tumor cell invasion in tissue-like ECMs.

Several experimental strategies have been reported to studythe regulation of tumor cell migration by ECM stiffness, porosity,or both. For example, polydimethylsiloxane (PDMS) microchan-nels of defined geometry have been used to simulate 3D matrixpores to study the dependence of cell migration on channel width(20–22). An important limitation of PDMS is that the stiffnessof this material exceeds that of most soft tissues, strongly limitingits utility as a model of these tissues. In collagen matrices thatspan a more physiologically relevant range of ECM stiffness, poresize has been modified by manipulating collagen concentration,pH, and gelation temperature (23), and by adding agarose (6).Although these collagen-based scaffolds do permit indirect con-trol of matrix porosity, their use is complicated by the fact thatthese manipulations also alter microscale and/or macroscale scaf-fold structure and mechanics. Moreover, most of these systemsrequire retrospective determination of pore size based on empiri-cal correlations and do not, in general, permit prospective impo-sition of some pore size of interest. As a way of addressing theselimitations, “bead templating” approaches have recently beendeveloped to yield hydrogels of defined stiffness containing acommunicating network of pores whose characteristic size isdictated by the particles around which the scaffold is formed (24).In practice, the conduits between pores are so short that cellsare observed to “jump” discontinuously between void chambers,offering limited opportunity to observe and characterize cells inconfined geometries. Thus, the field could significantly benefitfrom a matrix platform that allows independent manipulation ofECM stiffness and pore size and also enables the monitoring ofsustained cell migration in a confined microenvironment.

Here we present a culture platform for the study of tumor cellinvasion in which matrix stiffness and confinement (pore size)may be varied independently of one another. Our approach isbased on polymerization and gelation of defined-stiffness PAhydrogels around silicon-based scaffolds of defined microtopo-graphy, such that the surface of the PA gel adopts the inverse

Author contributions: A.P. and S.K. designed research; A.P. performed research; A.P.contributed new reagents/analytic tools; A.P. analyzed data; and A.P. and S.K. wrote thepaper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. D.E.D. is a guest editor invited by the EditorialBoard.1To whom correspondence should be addressed. E-mail: skumar@berkeley.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1118073109/-/DCSupplemental.

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contours of the master, resulting in channels of defined geometry.In other words, the elasticity of these micro-PA channels (μPACs)is entirely determined by the choice of PA formulation, and thechannel geometry is entirely dictated by the silicon master, withthe two subject to independent control. Using this μPAC plat-form, we investigated the relationship between ECM stiffness,pore size, and cell migration speed, with a specific focus onunderstanding how the regulation of cell migration on ECM stiff-ness is affected by the degree of matrix confinement. Our resultsdemonstrate that matrix confinement fundamentally alters theclassical biphasic relationship between ECM stiffness and migra-tion speed and that this phenomenology depends on nonmusclemyosin II (NMMII)-based contractility. We hypothesize that thiseffect originates from the fact that confinement forces polariza-tion of traction forces along a single dimension, and we test thishypothesis using a multiscale computational model of a cellmigrating through a pore of defined geometric and mechanicalproperties.

ResultsFabrication of μPAC Platform. To study cell migration in a systemin which ECM stiffness and confinement could be controlled in-dependent of one another, we combined photolithography tech-niques and controlled polymerization of PA hydrogels to con-struct microchannels of varying width embedded in PA gels ofspecified stiffness (microfabricated polyacrylamide channels, orμPACs, Fig. 1A). In this approach, we allowed a PA precursorsolution (acrylamide and bisacrylamide at a defined ratio plusinitiators TEMED and ammonium persulfate) to polymerize andgel against a microfabricated silicon master with predefined to-pographical patterns of variable channel width (cw). This proce-dure resulted in PA hydrogels spanning a range of stiffness valueswhose surfaces were marked with channels of defined size thatmatched the contours of the silicon master, analogous to pastuses of PA for micromolding applications (25, 26). We designedthe device to have ≥75-μm-thick walls between all channels tominimize mechanical transmission across the channel wall (27).We confirmed this expectation by using atomic force microscopy(AFM) to measure ECM stiffness in the plateau regions betweenwide and narrow channels (Fig. S1), which indeed verified thatECM stiffness was uniform across the surface of the device.We subsequently functionalized these scaffolds with full-lengthECM proteins to render them suitable for cell adhesion and mi-gration. The subsequent spontaneous migration of cells withinthe channels enabled us to track cell motility in μPACs of varyingstiffness and channel width over a period of several hours(Fig. 1B). Confocal microscopy revealed that cells in microchan-nels intimately associate with all three channel surfaces and formvinculin-positive adhesions on side walls, consistent with a 3Dmorphology (Fig. S2).

Enhanced Cell Migration in Narrow Channels. We began by investi-gating the dependence of migration speed of U373-MG humanglioma cells on channel stiffness and width by creating a series ofμPAC scaffolds in which stiffness was varied between 0.4 and120 kPa and channel width was varied between 10 and 40 μm,with unconstrained (flat) gels included as a control (Fig. 2 Aand B; these plots are the same dataset depicted two ways forclarity). We chose this stiffness range because it spans the regimeof maximal mechanosensitivity for human glioblastoma cells (8,28) and other mammalian cell types (10, 13, 14), and we chosethese channel widths in order to sample values on the same lengthscale as the cell. Somewhat surprisingly, for a fixed stiffness, weobserved that migration speed fell with increasing channel width(Fig. 2A), with the most pronounced confinement dependencebeing observed on the stiffest matrix (120 kPa). For a fixed porediameter, we observed a diversity of relationships between migra-tion speed and stiffness; specifically, migration speed varied

biphasically (i.e., passed through a single maximum) with stiffnessfor the two largest channel widths (cw ¼ 20 and 40 μm) andmonotonically increased with stiffness for the smallest channelwidth (cw ¼ 10 μm) (Fig. 2B). In narrow channels, migrationspeed increased but did not show biphasic behavior over therange of ECM stiffnesses examined; it is possible that a local max-imum may theoretically exist on significantly stiffer ECMs (i.e.,>150–200 kPa), but these stiffness values exceed both peak va-lues typically achieved with the PA system (8, 10, 12, 15) and thenormal stiffness range of almost all soft tissues (29). Importantly,we also observed a biphasic migration pattern on unconfinedECMs, consistent with our own and others’ previous observations(14, 19, 28). In other words, confinement not only increases mi-gration speed overall but also fundamentally alters the manner inwhich ECM stiffness governs migration speed. Phase contrastimaging provided additional insight into this observation and re-vealed that the degree to which a cell interacts with the channeldepends on channel width, with wide channels permitting cells topreferentially adhere to one channel wall and narrow channelsforcing cells to adhere to multiple walls and adopt the shapeof the channel (Fig. 2C and Movies S1 and S2).

Relationship Between Matrix Stiffness, Cell Polarization, and Migra-tion Speed. Given that very narrow channels promote cell polar-ization and also enhance migration speed, we next decided toinvestigate whether migration speed might correlate with cellpolarization on matrices lacking geometric constraints on cellpolarization: i.e., unconfined (flat) scaffolds (Figs. 3 and 4). Asdescribed earlier, migration speed depends biphasically on ECMstiffness (Fig. 2B). When we performed morphometric analysison these cells, we confirmed that, as expected, projected cell areaincreased with increasing matrix stiffness, with cells failing toengage the most compliant ECMs and spreading extensively onthe stiffest ECMs (Fig. 4D). Interestingly, however, we discoveredthat even though spreading area increased monotonically with

Fig. 1. Design and creation of microfabricated polyacrylamide channels(μPACs). (A) Schematic of process, including fabrication of a silicon masterwith topographic patterns of defined size and shape, formation of a PAhydrogel of prescribed elasticity around the features, separation of the PAhydrogel from the master, and seeding of cells. (B) Phase contrast imagesof device fabricated from 120 kPa PA hydrogel and containing channels com-posed of pores of varying dimensions. Scale bar ¼ 40 μm.

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ECM stiffness, cell polarization exhibited a biphasic dependenceon ECM stiffness, similar to migration speed (Fig. 3A). Specifi-cally, cells adopted isotropic morphologies on the softest andstiffest matrices (albeit with much different degrees of spreadingin each case) and a highly polarized, spindle-like morphologyon intermediate-stiffness matrices (Fig. 3 B–D). In other words,in the complete absence of geometric limitations on cell adhesionand spreading, morphological polarization predicts migrationspeed, with increases in one parameter correlated with increasesin the other.

Regulation of Cytoskeletal Architecture by Matrix Stiffness and Con-finement. To gain additional insight into the relationship betweenchannel width and cell polarization, we used confocal microscopyto visualize the intracellular distribution of phosphorylated myo-sin light chain (pMLC) and F-actin (Fig. 4 and Fig. S3). Cells inwide channels (cw ¼ 40 μm) and on flat (2D) substrates adoptedhighly spread morphologies compared to cells in narrow channels(cw ¼ 10 μm), with differences most apparent on the stiffestmatrices (120 kPa) (Figs. 4 A–D and Movies S1 and S2). More-over, automated image correlation analysis of F-actin and pMLCfluorescence revealed that cells on flat substrates and inside widechannels oriented their stress fibers in a much more radially uni-form fashion than cells in narrow channels regardless of matrixstiffness (Fig. 4 E and F), with stress fibers in narrow channelsstrongly coaligned with the long axis of the channel. Thus, just ason unconfined matrices, stress fiber alignment strongly predictsmigration speed, with the most highly aligned stress fibers—and fastest motility—observed in narrow, stiff channels. In otherwords, migration speed tracks with the degree to which actomyo-sin traction force is polarized along a single axis, which confine-ment in a narrow channel appears to promote.

Myosin II-based Traction Polarization is Essential for ConfinementSensitivity. Based on the preceding observations, we hypothesizedthat the enhanced migration rates in the narrowest channels re-sulted directly from enhanced polarization of actomyosin tractionforces in these scaffolds. If this hypothesis is correct, targeteddisruption of this polarization would be expected to offset thisenhanced migration. Inhibition of myosin II is known to disrupt

cytoskeletal coherence (30, 31) and abrogate stress fibers, both ofwhich are expected to be key to polarization of traction forces(Figs. 2 and 4). Thus, we repeated our studies in the presenceof the NMMII ATPase inhibitor blebbistatin (32) (Fig. 5). Con-focal imaging of F-actin distributions in blebbistatin-treated cellsconfirmed dissipation of stress fibers under all ECM conditions(Fig. S4). We then measured the migration speed of blebbistatin-treated cells for various ECM properties in our μPAC system(Fig. 5A), and found two important differences from the controlcase (Fig. 2). First, blebbistatin-treated cells migrated faster thancontrol cells for most ECM conditions.(Figs. 2B, and 5A, andFig. S5), similar to previous reports (8, 33, 34). This effect hasbeen attributed to the ability of NMMII to periodically interruptactin polymerization and hinder protrusions at the leading edge

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Fig. 2. Migration speed versus ECM stiffness andchannel width. (A) Migration speed versus channelwidth for soft, intermediate and stiff ECMs, corre-sponding to E ¼ 0.4, 10, and 120 kPa. *p < 0.05with respect to narrow (cw ¼ 10 μm) channels.(B) Migration speed versus ECM stiffness for nar-row, intermediate, and wide channels (cw ¼ 10,20, and 40 μm) and flat 2D gels. *p < 0.05 for pair-wise comparison between two indicated stiffnessvalues for all given channel widths, including 2Dflat gel. n > 35 cells per condition over multiplechannels and devices. (C) Phase contrast imagesof cells migrating inside channels of varying stiff-ness and width. Scale bar ¼ 40 μm.

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(35). Consistent with this role, we observed significantly longerprotrusions in blebbistatin-treated cells (Fig. 5B and Fig. S4) thanin untreated control cells (Figs. 2–4). Second, NMMII inhibitionfundamentally altered the role of channel width in modulatingthe relationship between migration speed and ECM stiffness.In untreated controls (Fig. 2), we had observed a biphasic depen-dence of migration speed on ECM stiffness in unconfined 2Dma-trices and wide channels, whereas migration speed increasedmonotonically with ECM stiffness in narrow channels in the stiff-ness range examined. Conversely, in the setting of NMMII inhi-bition, all ECM conditions gave rise to a biphasic or saturatingrelationship, with the strongest biphasic relationship observed inthe narrowest channels (Fig. 5A). This stark difference betweenblebbistatin-treated and untreated cells supports our hypothesisthat traction polarization critically underlies the ability of narrowchannels to increase migration speed and overcome motility lim-itations associated with stiff substrates. In other words, NMMIIinhibition renders migration speed significantly less sensitive toconfinement, a concept we quantify as “confinement sensitivity”and define as the difference between migration speed in wide andnarrow channels for a given matrix stiffness (Fig. 5C).

Computational Model of Migration in Channels of Defined Width andStiffness.Our experimental data are strongly consistent with a fra-mework in which NMMII-based polarization of actomyosin trac-tion forces is key to promoting rapid cell migration in narrowchannels. To integrate all of these parameters into a coherent,quantitative paradigm, we developed a predictive computationalmodel of a cell migrating in an ECM channel of defined widthand stiffness (SI Text, Fig. S6). Using this model, we calculatedmigration speed (v) as a function of myosin activation and com-

pared the model predictions with our experimental measure-ments on ECMs of defined stiffness and channel width. We alsosimulated the effects of high and low myosin activity for the con-trol and the myosin knockdown cases, respectively.

In the control cases (i.e., no NMMII inhibition), our model pre-dicted a biphasic dependence of migration speed on ECM stiffnesson flat 2D gels and wide channels (Fig. 6A), which is consistentwith our experiments (Fig. 2). The drag force (Fd) increased pro-portionally with ECM stiffness and cell size (36), which in turnreduced the migration speed on very stiff ECMs and causedthe predicted biphasicity for wide channels and 2D gels (see cw ≫10 μm in Fig. 6A). We could track concurrent changes in cellpolarization by defining a polarization factor (ψ , see SIMethods), which depends on cell size and ECM confinement. In2D-like settings (flat matrix or cw ≫ 10 μm), ψ falls, which in turnreduces the polarized traction force (ψFc) and thus reducesmigration speed. Conversely, narrow channels (cw ≈ 10 μm) im-pose constraints on cell spreading that increase the polarizationfactor (ψ) and thus also increase the polarized traction. Thisenhanced traction polarization inside narrow channels yieldedfaster migration than in wider channels (Fig. 6A) and abrogatedthe biphasic dependence of migration speed on ECM stiffness.

Upon NMMII inhibition, the net contractile force (Fc) felldramatically and reduced the impact of the polarized tractionterm (ψFc) on migration speed in SI Text, Eq. S5. Stated anotherway, the reduction in contractile force and traction polarizationassociated with NMMII inhibition offset any gains in traction po-larization associated with a narrow channel. As a result, migrationspeed was primarily dictated by ECM stiffness and thus variedbiphasically with ECM stiffness regardless of channel width(Fig. 6B). The model also predicted faster migration following

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F Fig. 4. Stress fiber alignment and spreading areaof cells in defined confinement. Confocal imagesof F-actin and pMLC distribution for U373-MG cellsin (A) narrow channels (cw ¼ 10 μm), (B) wide chan-nels (cw ¼ 40 μm), and (C) unconfined flat 2D gels ofvarying ECM stiffness. Scale bar ¼ 20 μm. (D) pro-jected cell area, (E) F-actin alignment, and (F) coalign-ment of pMLC immunofluorescence with channelaxis as a function of ECM stiffness for varying degreesof confinement. Statistically different pairs (p < 0.05)are indicated by horizontal square brackets. n > 12

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NMMII inhibition under all ECM conditions (Fig. 6), which wascaused by a drastic rise in protrusive force (Fp) due to the releaseof myosin-driven pauses in protrusions (35, 37). Additionally, weassumed that the number of protrusions at the leading edge of thecell would depend on cell area, which has been shown to increasewith channel width (Fig. 4D). We captured this behavior in themodel by prescribing a simple proportionality between the pro-trusive force and channel width, which in turn yielded higher mi-gration speed in wider channels (Fig. 6B) in NMMII-inhibitedcells where a protrusive mechanism was the most dominant reg-ulator of motility.

DiscussionThe invasion of a wide variety of tumors is strongly regulated bythe biophysical properties of the ECM, including ECM elasticityand microstructure. However, the field’s ability to dissect the dis-tinct contributions of these two parameters to tumor invasion andgain insight into the underlying molecular mechanisms has beenseverely limited by the absence of ECM scaffolds that enabletheir independent variation. The problem is further compoundedby the lack of computational models of cell motility that integratecellular adhesive and contractile mechanisms with ECM me-chanics and geometry. To address these unmet needs in a sys-tematic manner, we developed a unique microscale cultureplatform (μPACs) that enabled independent investigation ofthe effects of ECM stiffness and confinement on cell migration.As a result of these studies, we were able to show that matrix con-finement profoundly alters the dependence of cell migrationspeed on ECM stiffness. We attribute this result to the effectof ECM stiffness and channel width on polarization of tractionforce; while overall cellular actomyosin contractility increaseswith ECM stiffness, isotropic spreading of the cell in 2D-likesettings (wide channels) spatially defocuses traction forces andreduces the net propulsive force in the direction of cell migration.Physical constraint of cells to a narrow channel forces polariza-tion and alignment of these forces along the direction of the chan-nel and promotes faster cell migration for a given ECM stiffness.Thus, narrow channels permit cells to exploit the high tractionforces supported by stiff substrates without the loss of tractionpolarization associated with isotropic spreading observed onunconfined substrates. As a result, the fastest motility is observedin stiff, narrow channels.

Our work adds to a growing literature on the regulation ofmigration speed by ECM stiffness (8, 14, 28). A biphasic depen-dence of cell migration speed on ECM stiffness was first reported

for vascular smooth muscle cells (SMCs) (14), and we have re-ported (and confirmed here) a similar relationship for humanglioblastoma cells (28). Analogous to the biphasic dependenceof migration speed on ECM ligand density (5, 36) this relation-ship is typically explained in terms of the balance between trac-tion force generation and adhesion stability: Soft matrices do notsupport the traction forces needed for effective spreading and mi-gration, resulting in unstable punctate focal adhesions, whereasstiff matrices support such high traction forces that adhesionsare hyperstabilized to the point where they restrict motility.Consequently, an optimum migration exists at some intermediate

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Fig. 5. Effect of nonmuscle myosin II inhi-bition on cell motility. (A) Migration speedversus ECM stiffness for varying channelwidth. n > 30 cells per condition. (B) Phasecontrast images of cells inside narrow andwide channels and flat 2D gels of varyingstiffness. Scale bar ¼ 40 μm. (C) Confine-ment sensitivity, Δν, calculated as jνnarrow−νwidej, where νnarrow and νwide are averagerespective migration speeds for narrow(cw ¼ 10 μm) and wide (cw ¼ 40 μm) chan-nels versus ECM stiffness for control andblebbistatin-treated cells. Statistical signifi-cance (*p < 0.05) determined by Student’st test (unpaired, two-tailed, 95% confi-dence interval).

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ECM stiffness. Our data add to this understanding by elucidatingthe role of traction polarization, which is strongly affected both bystiffness and matrix confinement. Specifically, stiff ECMs reducetraction polarization by permitting isotropic spreading, but thiscan be overcome (rescued) by confining cells in narrow channelsthat force these traction forces to be highly aligned. Disruption ofthis polarization via myosin inhibition speeds motility and causesrecovery of biphasic behavior in narrow channels. These findingsalso build upon recent studies demonstrating that restriction ofcells to narrow ECM strips significantly increases migrationspeed, which may underlie the high, persistent motility rates ob-served in fibrillar ECMs (38, 39).

As more is understood about biophysical regulation of cellmotility in 3D ECMs, it is becoming clear that ECM mechanicsand architecture vary widely in both space and time, and that cellmigration is closely attuned to these variations (17, 40). Given thediverse biophysical properties of the matrix present in vivo, it iscritical to develop culture models that facilitate systematic in vitrodeconstruction of how these inputs drive cell migration. We havenow advanced these efforts by developing a paradigm for separ-ating the roles of ECM stiffness andmatrix confinement, using thissystem to discover a way to alter a previously established relation-ship between migration speed and ECM stiffness solely by varyingmatrix confinement, and identifying actomyosin contractility as anintracellular signaling pathway that enables confinement-medi-ated motility enhancement. We anticipate that the μPAC platformwill facilitate the study of even more complex variations in ECMconfinement and stiffness. Because of the high throughput andparallelizability of this microfluidic platform and its compatibility

with most standard microscopy methods, our system also retainssome of the key advantages of traditional 2D culture that mayeventually play a role in high-throughput screening of intracellularand extracellular factors that modulate 3D invasion.

Materials and MethodsSee SI Text for detailed descriptions of following methods: (a) Cell culture; (b)Live cell imaging and data analysis; (c) Immunofluorescence, confocal micro-scopy, and image analysis; (d) Statistical analysis; (e) Atomic force microscopy.

Fabrication of PA Microchannels. Silicon masters were fabricated using stan-dard photolithographic techniques (Fig. 1). A volume of PA precursor solutionsufficient to achieve a gel of approximately 100 μm thickness was placed be-tween a reactive glass surface and the siliconmold and allowed to polymerize.The PA precursor solutions were made as previously described (8) acrylamide/bisacrylamide (A/B) percentages of 4% A/0.2% B, 10% A/0.3% B, and 15% A/1.2% B corresponding to PA gels of elastic moduli of 0.4, 10, and 120 kPa(8, 15). Channel widths, cw , are reported with respect to the silicon master,not the final PA channels. See SI Text for a more detailed description.

Mathematical Model. Our model assumes that cell migration is a result of sev-eral subcellular mechanisms working in tandem: stabilization of adhesions,extension of protrusions, and generation of actomyosin contractility to over-come drag forces (5, 28), as illustrated in Fig. S6 and described in more detailin SI Text.

ACKNOWLEDGMENTS. This work was supported by grants to SK from the Na-tional Institutes of Health (Director’s New Innovator Award 1DP2OD004213and Physical Sciences-Oncology Center Award 1U54CA143836) and theNational Science Foundation (CMMI 1105539). Confocal images were ob-tained at the CIRM/QB3 Stem Cell Shared Facility.

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38. Doyle AD, et al. (2012) Microenvironmental control of cell migration: Myosin IIA isrequired for efficient migration in fibrillar environments through control of celladhesion dynamics. J Cell Sci, 10.1242/jcs.098806.

39. Doyle AD, Wang FW, Matsumoto K, Yamada KM (2009) One-dimensional topographyunderlies three-dimensional fibrillar cell migration. J Cell Biol 184:481–490.

40. Ananthanarayanan B, Kim Y, Kumar S (2011) Elucidating the mechanobiology ofmalignant brain tumors using a brain matrix-mimetic hyaluronic acid hydrogel plat-form. Biomaterials 32:7913–7923.

Pathak and Kumar PNAS ∣ June 26, 2012 ∣ vol. 109 ∣ no. 26 ∣ 10339

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